Y=3x^2-18x-2

Solution for Y=3x^2-18x-2 equation:

=3Y^2-18Y-2

We move all terms to the left:

-(3Y^2-18Y-2)=0

We get rid of parentheses

-3Y^2+18Y+2=0

a = -3; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-3)·2
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{87}}{2*-3}=\frac{-18-2\sqrt{87}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{87}}{2*-3}=\frac{-18+2\sqrt{87}}{-6}
$